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Complex Line integral of 1/z over the principle branch cut

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#integration #logarithms #branch-cuts #line-integrals
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Find the value of $x$ that satisfies the equation $\log_{10} \left(\frac{x^{\frac{1}{x}}}{x^{\frac{1}{x+1}}}\right) = 1/5050$ .

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#functions #logarithms
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What does $d\log\left(\frac{y}{x}\right)$ mean mathematically?

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#calculus #derivatives #notation #logarithms #differential
201
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Limit $\lim_{x\to\infty} x-x^{2}\ln\left(1+\frac{1}{x}\right)$

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#calculus #limits #logarithms
365
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integral of logarithm and rational function

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#calculus #integration #definite-integrals #logarithms
104
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Maclaurin series for a function

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#calculus #logarithms #taylor-expansion #exponential-function
123.1k
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How do I square a logarithm?

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#algebra-precalculus #logarithms
2.1k
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Integration of $\log(\sin x)$

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#integration #logarithms
137
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Solve this equation $4^{\log_2(x)}-2^{\log_2(x)}=3^{\log_3(12)}$.

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#algebra-precalculus #logarithms
296
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Solve this logarithmic equation: $2^{2-\ln x}+2^{2+\ln x}=8$

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#algebra-precalculus #logarithms #exponentiation #quadratics
218
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Solve the equation: $x^{1/(1+\log x)}=10^3$

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#logarithms
96
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Solve this equation: $\log_3(3-2\cdot3^{x+1})=2+2x$

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#logarithms
835
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Prove that $ln(x)$ is concave by using the following definition for $ln(x)$

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#real-analysis #integration #logarithms
567
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Real logarithm of a real matrix?

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#matrices #algorithms #logarithms #matlab #real-numbers
87
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Where to write the power with a logarithmic function?

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#logarithms

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